High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

DECENTRALIZED STABILIZATION OF LARGE-SCALE LINEAR INTERCONNECTED SYSTEMS WITH TIME-VARYING DELAYS

The decentralized stabilization conditions for large-scale linear interconnection systems with time-varying delays were established by using some different decomposition cases of interconnection matrices, and a method for designing the decentralized local memoryless state feedback controllers was proposed. All of the considered delays are continuous function, and satisfy some conditions.

Robust non-fragile control for discrete-delay nonlinear large-scale systems

Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.

Modified Augmented Lagrange Multiplier Methods for Large-Scale Chemical Process Optimization

Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.

Decentralized H-infinity state feedback control for discrete-time singular large-scale systems

The decentralized H-infinity control problem for discrete-time singular large-scale systems is considered. Based on the bounded real lemma of discrete-time singular systems, a sufficient condition for the existence of decentralized H-infinity controller for discrete-time singular large-scale systems is presented in terms of the solvability to a certain system of linear matrix inequalities by linear matrix inequality (LMI) approach, and the feasible solutions to the system of LMIs provide a parameterized representation of a set of decentralized H-infinity controller. The given example shows the application of the method.

Decentralized robust stabilization of discrete-time fuzzy large-scale systems with parametric uncertainties: a LMI method

Decentralized robust stabilization problem of discrete-time fuzzy large-scale systems with parametric uncertainties is considered. This uncertain fuzzy large-scale system consists of N interconnected T-S fuzzy subsystems, and the parametric uncertainties are unknown but norm-bounded. Based on Lyapunov stability theory and decentralized control theory of large-scale system, the design schema of decentralized parallel distributed compensation （DPDC） fuzzy controllers to ensure the asymptotic stability of the whole fuzzy large-scale system is proposed. The existence conditions for these controllers take the forms of LMIs. Finally a numerical simulation example is given to show the utility of the method proposed.

Non-fragile guaranteed cost control for uncertain neutral large-scale interconnected systems

This paper focuses on the problem of non-fragile decentralized guaranteed cost control for uncertain neutral large-scale interconnected systems with time-varying delays in state,control input and interconnections.A novel scheme,viewing the interconnections with time-varying delays as effective information but not disturbances,is developed.Based on Lyapunov stability theory,using various techniques of decomposing and magnifying matrices,a design method of the non-fragile decentralized guaranteed cost controller for unperturbed neutral large-scale interconnected systems is proposed and the guaranteed cost is presented.The further results are derived for the uncertain case from the criterion of unperturbed neutral large-scale interconnected systems.Finally,an illustrative example shows that the results are significantly better than the existing results in the literatures.

Research on Control Method of Inverters for Large-scale Grid Connected Photovoltaic Power System

A grid-connected inverter controlling method to analyze dynamic process of large-scale and grid-connected photovoltaic power station is proposed. The reference values of control variables are composed of maximum power which is the output of the photovoltaic array of the photovoltaic power plant, and power factor specified by dispatching, the control strategy of dynamic feedback linearization is adopted. Nonlinear decoupling controller is designed for realizing decoupling control of active and reactive power. The cascade PI regulation is proposed to avoid inaccurate parameter estimation which generates the system static error. Simulation is carried out based on the simplified power system with large-scale photovoltaic plant modelling, and the power factor, solar radiation strength, and bus fault are considered for the further research. It’s demonstrated that the parameter adjustment of PI controller is simple and convenient, dynamic response of system is transient, and the stability of the inverter control is verified.

Solving Severely Ill⁃Posed Linear Systems with Time Discretization Based Iterative Regularization Methods

Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced to linear systems.Due to the typical ill-posedness of inverse problems,the reduced linear systems are often illposed,especially when their scales are large.This brings great computational difficulty.Particularly,a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution.Therefore,regularization methods should be adopted for stable solutions.In this paper,a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems.An iterative scheme becomes a regularization method only when the iteration is early terminated.And a Morozov’s discrepancy principle is applied for the stop criterion.Compared with the conventional Landweber iteration,the new methods have acceleration effect,and can be compared to the well-known acceleratedν-method and Nesterov method.From the numerical results,it is observed that using appropriate discretization schemes,the proposed methods even have better behavior when comparing withν-method and Nesterov method.

Posterior Constraint Selection for Nonnegative Linear Programming

Posterior constraint optimal selection techniques (COSTs) are developed for nonnegative linear programming problems (NNLPs), and a geometric interpretation is provided. The posterior approach is used in both a dynamic and non-dynamic active-set framework. The computational performance of these methods is compared with the CPLEX standard linear programming algorithms, with two most-violated constraint approaches, and with previously developed COST algorithms for large-scale problems.

Constraint Optimal Selection Techniques (COSTs) for Linear Programming

We describe a new active-set, cutting-plane Constraint Optimal Selection Technique (COST) for solving general linear programming problems. We describe strategies to bound the initial problem and simultaneously add multiple constraints. We give an interpretation of the new COST’s selection rule, which considers both the depth of constraints as well as their angles from the objective function. We provide computational comparisons of the COST with existing linear programming algorithms, including other COSTs in the literature, for some large-scale problems. Finally, we discuss conclusions and future research.

A Dynamic Active-Set Method for Linear Programming

An efficient active-set approach is presented for both nonnegative and general linear programming by adding varying numbers of constraints at each iteration. Computational experiments demonstrate that the proposed approach is significantly faster than previous active-set and standard linear programming algorithms.

PRACTICAL STABILITY OF LINEAR DELAY SYSTEMS AND LARGE-SCALE DELAY SYSTEMS

The practical stability theory, an important branch of stability theory, has been developed as a meaningful quantitative theory for the analysis of systems on the basis of the early works of N. G. Chetayev (1935, 1960), N. D. Moiseyev (1945), G. E. Melnikov (1956), J. P. LaSalle and S. Lefschetz (1961), et al. The investigations on this topic are mostly with the ordinary differential systems and discontinuous systems.

基于GPU-CUDA的共轭斜量法实现及性能对比

偏微分方程数值解法(包括有限差分法、有限元法)以及大量的数学物理方程数值解法最终都会演变成求解大型线性方程组。因此,探讨快速、稳定、精确的大型线性方程组解法一直是数值计算领域不断深入研究的课题且具有特别重要的意义。在迭代法中,共轭斜量法(又称共轭梯度法)被公认为最好的方法之一。但是,该方法最大缺点是仅适用于线性方程组系数矩阵为对称正定矩阵的情况,而且常规的CPU算法实现非常耗时。为此,通过将线性方程组系数矩阵作转换成对称矩阵后实施基于GPU-CUDA的快速共轭斜量法来解决一般性大型线性方程组的求解问题。试验结果表明:在求解效率方面,基于GPU-CUDA的共轭斜量法运行效率高,当线性方程组阶数超过3000时,其加速比将超过14;在解的精确性与求解过程的稳定性方面,与高斯列主元消去法相当。基于GPU-CUDA的快速共轭斜量法是求解一般性大型线性方程组快速而非常有效的方法。

Fresh views on some recent developments in the simplex algorithm

First, the main procedures and the distinctive features of the most-obtuse-angle（MOA）row or column pivot rules are introduced for achieving primal or dual feasibility in linear programming. Then, two special auxiliary problems are constructed to prove that each of the rules can be actually considered as a simplex approach for solving the corresponding auxiliary problem. In addition, the nested pricing rule is also reviewed and its geometric interpretation is offered based on the heuristic characterization of an optimal solution.

A multilevel preconditioner and its shared memory implementation for a new generation reservoir simulator

As a result of the interplay between advances in computer hardware, software, and algorithm, we are now in a new era of large-scale reservoir simulation, which focuses on accurate flow description, fine reservoir characterization, efficient nonlinear/linear solvers, and parallel implementation. In this paper, we discuss a multilevel preconditioner in a new-generation simulator and its implementation on multicore computers. This preconditioner relies on the method of subspace corrections to solve large-scale linear systems arising from fully implicit methods in reservoir simulations. We investigate the parallel efficiency and robustness of the proposed method by applying it to million-cell benchmark problems.

Computation of Peak Output for Inputs Restricted in L_2 and L_∞ Norms Using Finite Difference Schemes and Convex Optimization

Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two- and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.

A Note on the Adaptive Simpler Block GMRES Method

The adaptive simpler block GMRES method was investigated by Zhong et al.(J Comput Appl Math 282:139-156, 2015) where the condition number of the adaptively chosen basis for the Krylov subspace was evaluated. In this paper, the new upper bound for the condition number is investigated. Numerical tests show that the new upper bound is tighter.

A FAST SIMPLEX ALGORITHM FOR LINEAR PROGRAMMING

Recently, computational results demonstrated remarkable superiority of a so-called ＂largest-distance＂ rule and ＂nested pricing＂ rule to other major rules commonly used in practice, such as Dantzig＇s original rule, the steepest-edge rule and Devex rule. Our computational experiments show that the simplex algorithm using a combination of these rules turned out to be even more efficient.

Recent Progress in Fiber-Optic Hydrophones

Fiber-optic hydrophone (FOH) is a significant type of acoustic sensor, which can be used in both military and civilian fields such as underwater target detection, oil and natural gas prospecting, and earthquake inspection. The recent progress of FOH is introduced from five aspects, including large-scale FOH array, very-low-frequency detection, fiber-optic vector hydrophone (FOVH), towed linear array, and deep-sea and long-haul transmission. The above five aspects indicate the future development trends in the FOH research field, and they also provide a guideline for the practical applications of FOH as well as its array.